Normalized Ground States for the Sobolev Critical Fractional Kirchhoff Equation with at Least Mass Critical Growth

In this paper, we delve into the following nonlinear fractional Kirchhoff-type problem (a+b||(−Δ)s2u||22)(−Δ)su+λu=g(u)+|u|2s*−2u in R3 with prescribed mass ∫R3|u|2dx=ρ>0, where s∈(34,1),λ∈R,2s*=63−2s. Under some general growth assumptions imposed on g, we employ minimization of the energy functional on the linear combination of Nehari and Pohoz˘aev constraints intersected with the closed ball in the L2(R3) of radius ρ to prove the existence of normalized ground state solutions to the equation. Moreover, we provide a detailed description for the asymptotic behavior of the ground state energy map.